Laboratoire de Mécanique des Fluides et d'Acoustique - UMR 5509

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Accueil > Pages perso > Bos Wouter > Research

ANR Project 2021-2025


Characteristic Mapping Method for the Euler Equations


Project Partners
Kai Schneider (PI, Aix-Marseille University),
Jean-Christophe Nave (McGill University, Canada),
Benjamin Kadoch (Aix-Marseille University),
Wouter Bos

Even though computational resources grow rapidly, the extremely fine scales in fluid and plasma turbulence remain beyond reach using existing numerical methods. A combination of computational power and ingenious physical insights is usually needed to go beyond the brute force limit. We propose here to develop a novel numerical method, a fully Adaptive Characteristic Mapping Method (ACMM) for evolving the flow map, which yields exponential resolution in linear time. First results for the two-dimensional (2D) incompressible Euler equations show the extremely high resolution capabilities of the scheme obtained by decomposing the flow map and appropriate remapping.

The project consists of two parts. Part one is focused on the development of ACMM for 2D systems, including its adaptive version using multiresolution techniques and subsequently its application to 2D Euler flows, passive scalar mixing and magnetic reconnection problems. In the second part, we will extend the method to three dimensions (3D) and investigate the formation of singularities and turbulent dissipation.

Ref. X.Y. Yin, O. Mercier, B. Yadav, K. Schneider and J.-C. Nave.
A Characteristic Mapping Method for the two-dimensional incompressible Euler equations. J. Comput. Phys., 424, 109781, 2021